Question

solve using elimination.
9x + 7y = -19
-5x - 4y = 11
(\square, \square)
submit

Explanation:

Step1: Multiply equations to eliminate a variable

To eliminate \(y\), multiply the first equation by \(4\) and the second equation by \(7\).
First equation: \(4\times(9x + 7y)=4\times(-19)\) gives \(36x + 28y=-76\)
Second equation: \(7\times(-5x - 4y)=7\times11\) gives \(-35x - 28y = 77\)

Step2: Add the two new equations

Add the two equations: \((36x + 28y)+(-35x - 28y)=-76 + 77\)
Simplify: \(36x-35x+28y - 28y=1\) which gives \(x = 1\)

Step3: Substitute \(x = 1\) into an original equation

Substitute \(x = 1\) into \(9x+7y=-19\): \(9\times1+7y=-19\)
Simplify: \(9 + 7y=-19\)
Subtract \(9\) from both sides: \(7y=-19 - 9=-28\)
Divide by \(7\): \(y=\frac{-28}{7}=-4\)

Answer:

\((1, -4)\)